Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
Integer division is expensive. Much more expensive than multiplication. Much, much more expensive than addition. If you’re trying to make some integer operations really fast it’s bad news if you need to do division.
For every n, there is a base b such that n! = b^n. The relation between n and b(n) is surprisingly close to linear.
The logic behind Bézier Curves used in CSS animations and visual elements.
A Lindemayer system or LSystem for short consists of an alphabet of symbols that can be used to make strings, a collection of production that expand each symbol into some larger string of symbols, an initial “axiom” string from which to begin construction, and a mechanism for translating the generated strings into…
When you think about the Fibonacci sequence, you probably imagine a swirling vortex of oscillating points stretching outwards to infinity: Okay, no, obviously you don’t. Yet.
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
Fast Fibonacci Computations With a Linear Algebra Twist
This week we (me & Anton Kovsharov) published Paperproof, a Gentzen-tree-like proof interface for Lean 4. In this post I'll review proof visualisations from o...
Beneath the utilitarian purpose of computation, computing is also a source of delight and wonder . Software is not just databases and mail merges or SaaS and spreadsheets; it's creative coding and simulated cities , code poetry and bulletin board systems . It's websites that dazzle and iPhone apps that make the heart…
The myth A few years ago I saw a StackOverflow question (but I cannot find it now): allegedly Andrew Gelman blogged that Bayesian models would not overfit and would only underfit (I also cannot find Andrew’s blog post now but I think what he meant by “Bayesian models only underfits” is that you can never fully model…
The uncanny resemblance between double descent and a 50 year old theory from psychology
A dimension is a physical quantity that can be measured, while a unit is a specific amount of a physical quantity. For example, time is a dimension, which can be measured in temporal units such as hours or seconds.
The following Python function computes the Fibonacci sequence , without loops, recursion or floating point arithmetic:
In this blog post, we explore Spotify's journey from using the Fisher-Yates shuffle to a more sophisticated song shuffling algorithm that prevents clustering of tracks by the same artist. We then connect this challenge to Fibonacci hashing, and propose a novel, evenly distributed artist shuffling method.
Get up close and personal with Schnorr and his now patent-free linear signature algorithm.
We thought we were accelerating fast enough. Turns out we weren't.
Statistical arbitrage (stat arb) is a pillar of quantitative trading that relies on mean reversion to predict the future returns of an asset. Mean reversion believes that if a stock has risen higher it’s more likely to revert in the short term which is the opposite of a momentum strategy that believes if a stock has…
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
In 2005, id Software released the source code for their 1999 game Quake III Arena under the GPL-2 license. In the file code/game/q_math.c , there is a function for calculating the reciprocal square root of a number which at first glance seems to use a very peculiar algorithm:
A self-contained introduction to Gröbner bases and solving polynomial systems
On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. 1 2 3 4
Generative AI tools like ChatGPT and Midjournery are able to replicate (and often exceed) human-like performance on tasks like taking exams, generating text and making art.
This is the first part of a series of posts on big changes for SymPy with particular focus on speed. What I am going to describe in these posts are:
The fun of owning rural property is that knowing where your land actually starts and ends is a guess usually. Sure, you have a parcel description, and maybe even an online service with “official” GIS boundaries (for us here in New Brunswick, this is GeoNB ). However, since it’s in the middle of the forest, the odds of…
Originally developed by Aristid Lindenmayer in 1968, an L-System is a formalism to generate self-similar structures. Although, L-Systems are capable of generating famous fractals like the Sierpinski Triangle (Axiom: FXF--FF--FF, F → FF , X → --FXF++FXF++FXF-- , angle = 60 ) or the Gosper Curve (Axiom: FX, X →…
